Accepted Answer

You can upgrade weapons and armors at blacksmiths and campfires once you buy the kits from the first blacksmith that's near the Bell Gargoyles. To Modify your equipment you have to find Embers hidden throughout the world and bring them to one of the four blacksmiths to be able to create new and more powerful weapons. (also to note is that an Ember can only be used by a certain blacksmith, so if one can't use it you have to find the one that can)

As for the '+' you're talking about I'm assuming it's the info by the damage, like Physical 180 +60 (or some such number). The '+' damage is affected by the ParamBonus. So say if your weapon has a STR bonus of C, your weapon will become more powerful as you upgrade your Strength. The higher the Bonus the more the stat it is under will benefit the weapon.

The Drake sword will last you quite a while, but it will become obsolete. I'd say around 30 or so, or once you get to Sen's Fortress, is where you'll trade it in. You can find a nice Lightning Spear in Sen's that will do a lot of damage. Or you will find a weapon that has bonuses that apply to your build.

Other Answers

when looking at the stats for a piece of weapon or you have the base attack and the + stats. the + stats are based on the four icons on the weapon stat screen which represent str dex int and faith. If i remember correctly the drake sword has a base attack of 200 but no growth. I don't recommend using drake scales to upgrade the drake sword because its a waste. My character in my game was melee heavy weapons type. most of my points were pumped into str and en. en was so i had more stamina and could wear heavier armor. the heavier armors have higher poise which is the stat that determines whether you can be interrupted or not as you swing your weapon while being hit. this is important if you use heavier weapons and have slow attacks. I recommend looking at your stats and figuring what kind of character you want to play and specializing in certain stats. My character for example like i said has high str and en, average dex and mediocre int and faith. Then based on those stats figure out a weapon thats right for you. I chose man serpent greatsword after the drake sword wasnt cutting it anymore. I upgraded the man-serpent great sword to the +5 version as soon as i had a chance. the +5 version had a base attack of 165 which is lower than the drake sword but it was rated B in str growth. so as my str kept increasing from leveling so did the attack bonus to my greatsword. I actually used this sword for most of the game eventually upgrading it all the way to the +15 version which stats are 275 base and str B. I was doing around 4-500 dmg per swing. and it will continue to grow if i keep pumping more points into str. There are other builds you can try. different weapons have better growth in other stats. Daggers for example have great dex growth. their low attacks are made up for in how often they hit. anyways hope this helps